An accurate description of a seismic source signature is required in order to carry out a number of functions in seismic data processing. For example, source de-signature, deghosting, zero-phasing or de-bubbling, may be carried out using far-fields derived for a seismic source, which may be one-dimensional (1D), two-dimensional (2D) or three-dimensional (3D). This may require generating far-field signatures in the vertical direction or at a plurality of different take-off angles and azimuths. Seismic sources in marine surveys include arrays of individual or clustered air guns mounted on several parallel strings. Modelling of these seismic sources generates far-field signatures using, for example modelling packages such as Nucleus and Gundalf. These packages use source array geometry and gun characteristics to generate the far-field behaviour using physical modelling of air-guns and super-position of the resulting signatures, including air-gun interaction. These packages, however, are not able to reproduce the low frequency behaviour of the source arrays reliably.
Ziolkowski in Ziolkowski et al., “The signature of an Air Gun Array: Computation from Near Field Measurements Including Interactions”, Geophysics, Vol. 47, No. 10, pp. 1413-1421 (October 1982) and Parkes et al., “The Signature of an Air Gun Array: Computation from Near-Field Measurements Including Interactions—Practical Considerations, Geophysics, Vol. 48, No. 2, pp. 105-111 (February 1984) proposed the inversion of data obtained from near-field hydrophone (NFH) sensors mounted on the source array in the vicinity of the seismic air-guns, i.e., in the near-field, to obtain the source signature characteristics. Key to the methodology is the definition of notional sources as source signatures in the proximity of individual air guns within the seismic source array but taking the interactions between the bubbles that take place when the guns are fired together into account. These notional sources are used to generate the source array signatures as desired.
For legacy surveys, however, NFH recordings may be unavailable, and NFH data on current surveys may be contaminated. The use of contaminated NFH data would result in contaminated far-fields which could be unsatisfactory for their intended purpose. Attempts to overcome unavailable or contaminated data include the direct recording of a far-field from a sensor mounted on a rope and towed below the boat, which is not always practical. Therefore, a need still exists to calculate far-fields for sources when near-field data are unavailable or unreliable.